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# homotopy groupoids and crossed complexes: non-commutative structures in higher dimensional algebra (HDA)

# 0.1 Fields Institute 2004 Workshop on Categorical Structures for Descent–Galois Theory, Hopf Algebras and Semiabelian Categories

This is the topic of a series of papers that were published in 2004 on “Categorical Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories.” that appeared
as part of the *Proceedings of the Fields Institute Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories*, [1].

# 0.1.1 Homotopy Groupoids and Crossed Complexes provide tools for Solving Local-to-Global Problems: Non-commutative Structures in Higher Dimensional Algebra(HDA)

Among these remarkable mathematical contributions is an interesting paper on crossed complexes and homotopy groupoids as non-commutative tools for higher dimensional local-to-global problems. In this paper it was pointed out that
*“the structures which enable the full use of crossed complexes as a tool in algebraic topology are substantial, intricate and interrelated”*. These applications of crossed complexes are also closely connected with the concept of
double groupoid.

# References

- 1
PFIWCS-2004.
*Proceedings of the Fields Institute Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories*., September 23-28, 2004, published in the*Fields Institute Communications 43, (2004)*. - 2
R. Brown et al. “Crossed complexes and homotopy groupoids as non-commutative tools for higher dimensional local-to-global problems”, in
*Fields Institute Communications 43:101-130 (2004)*, (PDF and ps documents at arXiv/ math.AT/0212274).

## Mathematics Subject Classification

18D25*no label found*18D20

*no label found*18D15

*no label found*18C10

*no label found*18A40

*no label found*18A30

*no label found*18A25

*no label found*18-00

*no label found*18A20

*no label found*18A15

*no label found*55U35

*no label found*18D05

*no label found*

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